This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Solutions to problems from section 1.3 4. Let u = bracketleftbigg 3 2 bracketrightbigg and v = bracketleftbigg 2 1 bracketrightbigg . Display the following vectors using arrows on an xygraph: u , v , v , 2v , u + v , u v , and u 2v . Solution: 6. Write a linear system which is equivalent to x 1 bracketleftbigg 2 3 bracketrightbigg + x 2 bracketleftbigg 8 5 bracketrightbigg + x 3 bracketleftbigg 1 6 bracketrightbigg = bracketleftbigg bracketrightbigg Solution: 2 x 1 + 8 x 2 + x 3 = 0 , 3 x 1 + 5 x 2 6 x 3 = 0 . 10. Write a vector equation that is equivalent to the following linear sys tem: 4 x 1 + x 2 + 3 x 3 = 9 , x 1 7 x 2 2 x 3 = 2 , 8 x 1 + 6 x 2 5 x 3 = 15 . Solution: x 1 4 1 8 + x 2 1 7 6 + x 3 3 2 5 = 9 2 15 12. Is b a linear combination of a 1 , a 2 , and a 3 where a 1 = 1 2 2 , a 2 = 5 5 , a 3 = 2 8 , b =  5 11 7 ? Solution: Answering this question is the same as answering whether or not the linear system with augmented matrix 1 0 2 5 2 5 0 11 2 5 8 7 is consistent. Lets row reduce....
View
Full
Document
This note was uploaded on 01/28/2010 for the course MATH 307 taught by Professor Axenovich during the Fall '08 term at Iowa State.
 Fall '08
 AXENOVICH
 Vectors

Click to edit the document details